Does a diminished unison really exist?

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Does a diminished unison really exist?

Post by dannemoller » Mon Jul 10, 2017 5:32 pm

Hi!

When I teach my classes I tell them that there's no such thing as a diminished unison (or "förminskad prim", as we call it in Swedish). A perfect unison is the same note, and you can't decrease the distance between it, only increase it.

But in Dorico I find that the term "diminished unison" is used to transpose a note half a step downwards. It should properly be called transposing a note an augmented unison downwards.

Or are there differing traditions regarding unisons?

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Re: Does a diminished unison really exist?

Post by R Pearl » Mon Jul 10, 2017 5:57 pm

I teach the same thing - if my students can actually create a diminished unison, then they have been able to decrease the size of nothing. If they can do that, then they really don't need a degree in anything!

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Re: Does a diminished unison really exist?

Post by stringtapper » Mon Jul 10, 2017 6:05 pm

I also teach the same. It's a fun trick question.

The theory professor of mine who first brought it up joked that if a diminished unison existed it would tear a hole in time and space. :-)

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Re: Does a diminished unison really exist?

Post by Claude Lapalme » Mon Jul 10, 2017 6:13 pm

If a diminished unison is played in the forest but no music theorist is there to hear it, does it still make a sound?
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Re: Does a diminished unison really exist?

Post by Derrek » Mon Jul 10, 2017 7:13 pm

"The sound of one pitch flapping"?
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Daniel at Steinberg
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Re: Does a diminished unison really exist?

Post by Daniel at Steinberg » Mon Jul 10, 2017 9:38 pm

If you transpose C by a diminished unison, you'll get C flat, and if you transpose it by an augmented unison, you'll get C sharp.

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Re: Does a diminished unison really exist?

Post by JulianBennettHolmes » Mon Jul 10, 2017 9:52 pm

Daniel at Steinberg wrote:If you transpose C by a diminished unison, you'll get C flat, and if you transpose it by an augmented unison, you'll get C sharp.
I don't really understand that. I see that Dorico works this way, but I think the result is actually an augmented unison downwards, not a diminished unison.
The way the transpose dialog works for this is confusing to me — I'd rather ask it to transpose downwards by an augmented unison, rather than ask it to transpose by a diminished unison, which is an interval I don't believe actually exists.

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Re: Does a diminished unison really exist?

Post by MarkSealey » Mon Jul 10, 2017 10:54 pm

Is the key (no pun intended) to this the distinction between the interval itself, and actually transposing by the number of steps shared by that interval?

Just as you can add, say, '-5' to any integer, positive or negative:

-5 + -5 is different from 5 + -5…
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Re: Does a diminished unison really exist?

Post by Rob Tuley » Tue Jul 11, 2017 12:02 am

Diminished and augmented octaves definitely exist. (CPE Bach was very fond of diminished octaves).

So, what other name would you give to the (semitone) interval between C and C flat, to distinguish it from C to B?

(I suppose you could call it an "inverted augmented unison" :roll:)

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Re: Does a diminished unison really exist?

Post by R Pearl » Tue Jul 11, 2017 1:13 am

An interval is a measure of distance - C to C# is a unison that has been made larger, i.e., the interval has been augmented; same if you go from C to Cb - the distance increased. They are both augmented unisons. You can't diminish nothing, or put another way, you can't reduce the number of half steps if you begin with 0.

Ok, off the high horse now.

As long as we know how Dorico thinks, then we can adjust accordingly.

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Re: Does a diminished unison really exist?

Post by Binkeys » Tue Jul 11, 2017 2:08 am

Think of it like "negative harmony" (getting a lot of attention nowadays thanks to Jacob Collier).

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Re: Does a diminished unison really exist?

Post by JulianBennettHolmes » Tue Jul 11, 2017 2:20 am

R Pearl wrote:An interval is a measure of distance - C to C# is a unison that has been made larger, i.e., the interval has been augmented; same if you go from C to Cb - the distance increased. They are both augmented unisons. You can't diminish nothing, or put another way, you can't reduce the number of half steps if you begin with 0.
I think this is exactly right. And Rob Tuley has it right also — the name for the interval we're talking about it inverted augmented unison, or just an augmented unison down.

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Re: Does a diminished unison really exist?

Post by Claude Lapalme » Tue Jul 11, 2017 2:37 am

I sure hope there are no alien civilisations presently judging our species solely by studying this thread! ;)
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Re: Does a diminished unison really exist?

Post by Robby Poole » Tue Jul 11, 2017 3:10 am

I think this only applies, if you believe a unison is 0.

I am sure there are some who wouldn't think of a unison as 0.

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Re: Does a diminished unison really exist?

Post by Rob Tuley » Tue Jul 11, 2017 3:28 am

JulianBennettHolmes wrote:And Rob Tuley has it right also — the name for the interval we're talking about it inverted augmented unison, or just an augmented unison down.
Well, you may think I'm right, but I don't. IMO that name is almost as sensible as defining every diatonic chord as an inversion of the Dominant 13th with most of the notes missing 8-)

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Re: Does a diminished unison really exist?

Post by JulianBennettHolmes » Tue Jul 11, 2017 3:31 am

Robby Poole wrote:I think this only applies, if you believe a unison is 0.

I am sure there are some who wouldn't think of a unison as 0.
If not 0, then what do you suggest? Set theorists certainly consider a perfect unison to be 0.

I think the question is whether you consider a diminished interval to be one semitone smaller than the regular interval, or one semitone closer to 0.
-1 is smaller than 0, but it is obviously further away from 0 than 0 is.

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Re: Does a diminished unison really exist?

Post by MarkSealey » Tue Jul 11, 2017 3:50 am

I'd hope they'd be fascinated, and approve. The stuff of debate :-).
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Re: Does a diminished unison really exist?

Post by Rob Tuley » Tue Jul 11, 2017 8:40 am

Robby Poole wrote:I think this only applies, if you believe a unison is 0.

I am sure there are some who wouldn't think of a unison as 0.

Robby
It took a very long time before anybody was convinced that "0" was a number, and Europe was about the last place to "get it" as an idea, more than 1000 years after the Indians, ancient Egyptians and Babylonians, Chinese, Mayans, etc.

But we got there in the end - well, most of us did ;)

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Re: Does a diminished unison really exist?

Post by dannemoller » Tue Jul 11, 2017 8:48 am

R Pearl wrote:An interval is a measure of distance - C to C# is a unison that has been made larger, i.e., the interval has been augmented; same if you go from C to Cb - the distance increased. They are both augmented unisons. You can't diminish nothing, or put another way, you can't reduce the number of half steps if you begin with 0.
This is exactly what I mean, only expressed a lot better. :)

Now I know how it works in Dorico, but it actually took me a couple of moments to figure it out, so in a perfect world this should be corrected in the program, but it's no big deal!

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Re: Does a diminished unison really exist?

Post by filter55 » Tue Jul 11, 2017 12:36 pm

Claude Lapalme wrote:I sure hope there are no alien civilisations presently judging our species solely by studying this thread! ;)
Better be jugded by this thread than by a lot of "so sad" things going on nowadays.

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Re: Does a diminished unison really exist?

Post by david-p » Tue Jul 11, 2017 7:17 pm

Robby Poole wrote:I am sure there are some who wouldn't think of a unison as 0.

Robby
I am one of them...

If C to E is a third (3)
& C to D is a second
then C to C must logically be a first (1), or what we call a unison.

To my way of thinking, this leaves no option of a zeroth (0).

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Re: Does a diminished unison really exist?

Post by JulianBennettHolmes » Tue Jul 11, 2017 7:20 pm

david-p wrote:If C to E is a third (3)
& C to D is a second
then C to C must logically be a first (1), or what we call a unison.

To my way of thinking, this leaves no option of a zeroth (0).
Even with this logic, it still doesn't make sense. In this case, would a diminished unison be ½? Would a minor third be 2.5? This is one of the reasons integer notation was invented.

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Re: Does a diminished unison really exist?

Post by Thomas Eberth » Tue Jul 11, 2017 7:43 pm

The englisch version of Wikipedia knows the diminished unison and tells about sources.
The german version of Wikipedia knows the "verminderte Prim" and gives an example.

I think it's rather theoretical, but as a mathematician I would call it logical. .

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Re: Does a diminished unison really exist?

Post by R Pearl » Tue Jul 11, 2017 8:01 pm

The problem with interval names, i.e., using numbers, is that we have enharmonic spelling:
C-Db is a minor second, or a second due to D being the second letter in the alphabetic sequence. Hence C-C is a unison, but so is C-C#, but that is not by virtue is its distance, but of its spelling. We could avoid all this my naming intervals discretely and uniquely (no more Aug 4/dim5). I vote for formal names: Bob, Ted, Irving, Leopold, and so forth. Rather than "a P4th above B" it would be an "Irving above B."

I'm on to somethin'....

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Re: Does a diminished unison really exist?

Post by Rob Tuley » Tue Jul 11, 2017 8:12 pm

JulianBennettHolmes wrote:Even with this logic, it still doesn't make sense.
The convention of counting both ends of the range of an interval as different notes is consistent with the ancient Roman method of counting, and medieval music theory was controlled by the church, which of course worked exclusively in the Latin language. Like the ancient Greeks, the Romans did not recognize "zero" as a number at all.

This leads to the illogical situation (compared with contemporary mathematics) that an "octave" contains 8 diatonic steps, but a double-octave only contains 15, not 16.

In fact, the logical solution would be for an "octave" to contain 7, and a double-octave to contain 14. The interval from C to D would then be a "first", not a "second", and a "unison" would contain zero steps.

But since the term "octave has been used for at least 1000 years, nothing is likely to change any time soon!

(Note, the Catholic church still uses the term "octave" to refer to a full week of days starting and ending on days of the same name - e.g. Monday to Monday inclusive. This follows the same counting system.)

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